THE LOGIC OF CAUSATION

Phase Two: Microanalysis

Chapter 14 Main Three-Item Syllogisms

1. Applying Microanalysis to Syllogism.

2. The Moduses of Premises.

Putting the data in the above table together in various combinations, we can now ascertain the moduses of resulting conclusions. As already said, when the premises have no common modus, they are “inconsistent”. When some resulting modus(es) fall under causation (c) and some other(s) under non-causation (not-c), we must admit that there is “no conclusion”. In all other cases, there is a conclusion, namely the determination (whatever it be, at least causation or non-causation) which includes all the resulting moduses.

The following table lists all these results. Note well that all weak determinations mentioned in it are intended as absolute, though not so specified. Syllogism with relative weaks will be considered later.

Table 14.4. Moduses of conclusions of all syllogisms with strong or absolute weak positive premises, generic or joint.

 Major Minor Conclusion Common moduses No. First Figure Mood QR PQ PR 111 mn mn mn 130 1 112 mn mq mq 138 1 113 mn np np 146 1 114 mn pq pq 154 1 115 mn m m 130, 138 2 116 mn n n 130, 146 2 117 mn p p 146, 154 2 118 mn q q 138, 154 2 121 mq mn mq 132 1 122 mq mq mq 140 1 123 mq np no conclusion 147-148, 162, 164, 178-180 7 124 mq pq not-n 155-156, 170, 172, 186-188 7 125 mq m mq 132, 140 2 126 mq n no conclusion 132, 147-148, 162, 164, 178-180 8 127 mq p no conclusion 147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188 14 128 mq q not-n 140, 155-156, 170, 172, 186-188 8 131 np mn np 194 1 132 np mq no conclusion 74, 78, 134, 142, 198, 202, 206 7 133 np np np 210 1 134 np pq not-m 90, 94, 150, 158, 214, 218, 222 7 135 np m no conclusion 74, 78, 134, 142, 194, 198, 202, 206 8 136 np n np 194, 210 2 137 np p not-m 90, 94, 150, 158, 210, 214, 218, 222 8 138 np q no conclusion 74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222 14
 141 pq mn pq 196 1 142 pq mq not-n 76, 80, 136, 144, 200, 204, 208 7 143 pq np not-m 211-212, 226, 228, 242-244 7 144 pq pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 49 145 pq m not-n 76, 80, 136, 144, 196, 200, 204, 208 8 146 pq n not-m 196, 211-212, 226, 228, 242-244 8 147 pq p no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 56 148 pq q no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 151 m mn m 130, 132 2 152 m mq mq 138, 140 2 153 m np no conclusion 146-148, 162, 164, 178-180 8 154 m pq not-n 154-156, 170, 172, 186-188 8 155 m m m 130, 132, 138, 140 4 156 m n no conclusion 130, 132, 146-148, 162, 164, 178-180 10 157 m p no conclusion 146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188 16 158 m q not-n 138, 140, 154-156, 170, 172, 186-188 10 161 n mn n 130, 194 2 162 n mq no conclusion 74, 78, 134, 138, 142, 198, 202, 206 8 163 n np np 146, 210 2 164 n pq not-m 90, 94, 150, 154, 158, 214, 218, 222 8 165 n m no conclusion 74, 78, 130, 134, 138, 142, 194, 198, 202, 206 10 166 n n n 130, 146, 194, 210 4 167 n p not-m 90, 94, 146, 150, 154, 158, 210, 214, 218, 222 10 168 n q no conclusion 74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222 16 171 p mn p 194, 196 2 172 p mq no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208 14 173 p np not-m 210-212, 226, 228, 242-244 8 174 p pq no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 175 p m no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208 16 176 p n not-m 194, 196, 210-212, 226, 228, 242-244 10
 177 p p no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 64 178 p q no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 70 181 q mn q 132, 196 2 182 q mq not-n 76, 80, 136, 140, 144, 200, 204, 208 8 183 q np no conclusion 147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244 14 184 q pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 185 q m not-n 76, 80, 132, 136, 140, 144, 196, 200, 204, 208 10 186 q n no conclusion 132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244 16 187 q p no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 70 188 q q no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 64 Second Figure Mood RQ PQ PR 211 mn mn mn 130 1 212 mn mq mq 138 1 213 mn np np 146 1 214 mn pq pq 154 1 215 mn m m 130, 138 2 216 mn n n 130, 146 2 217 mn p p 146, 154 2 218 mn q q 138, 154 2 221 mq mn np 194 1 222 mq mq no conclusion 74, 78, 134, 142, 198, 202, 206 7 223 mq np np 210 1 224 mq pq not-m 90, 94, 150, 158, 214, 218, 222 7 225 mq m no conclusion 74, 78, 134, 142, 194, 198, 202, 206 8 226 mq n np 194, 210 2 227 mq p not-m 90, 94, 150, 158, 210, 214, 218, 222 8 228 mq q no conclusion 74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222 14
 231 np mn mq 132 1 232 np mq mq 140 1 233 np np no conclusion 147-148, 162, 164, 178-180 7 234 np pq not-n 155-156, 170, 172, 186-188 7 235 np m mq 132, 140 2 236 np n no conclusion 132, 147-148, 162, 164, 178-180 8 237 np p no conclusion 147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188 14 238 np q not-n 140, 155-156, 170, 172, 186-188 8 241 pq mn pq 196 1 242 pq mq not-n 76, 80, 136, 144, 200, 204, 208 7 243 pq np not-m 211-212, 226, 228, 242-244 7 244 pq pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 49 245 pq m not-n 76, 80, 136, 144, 196, 200, 204, 208 8 246 pq n not-m 196, 211-212, 226, 228, 242-244 8 247 pq p no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 56 248 pq q no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 251 m mn n 130, 194 2 252 m mq no conclusion 74, 78, 134, 138, 142, 198, 202, 206 8 253 m np np 146, 210 2 254 m pq not-m 90, 94, 150, 154, 158, 214, 218, 222 8 255 m m no conclusion 74, 78, 130, 134, 138, 142, 194, 198, 202, 206 10 256 m n n 130, 146, 194, 210 4 257 m p not-m 90, 94, 146, 150, 154, 158, 210, 214, 218, 222 10 258 m q no conclusion 74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222 16 261 n mn m 130, 132 2 262 n mq mq 138, 140 2 263 n np no conclusion 146-148, 162, 164, 178-180 8 264 n pq not-n 154-156, 170, 172, 186-188 8 265 n m m 130, 132, 138, 140 4 266 n n no conclusion 130, 132, 146-148, 162, 164, 178-180 10 267 n p no conclusion 146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188 16 268 n q not-n 138, 140, 154-156, 170, 172, 186-188 10 271 p mn q 132, 196 2 272 p mq not-n 76, 80, 136, 140, 144, 200, 204, 208 8
 273 p np no conclusion 147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244 14 274 p pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 275 p m not-n 76, 80, 132, 136, 140, 144, 196, 200, 204, 208 10 276 p n no conclusion 132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244 16 277 p p no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 70 278 p q no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 64 281 q mn p 194, 196 2 282 q mq no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208 14 283 q np not-m 210-212, 226, 228, 242-244 8 284 q pq no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 285 q m no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208 16 286 q n not-m 194, 196, 210-212, 226, 228, 242-244 10 287 q p no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 64 288 q q no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 70 Third Figure Mood QR QP PR 311 mn mn mn 130 1 312 mn mq np 146 1 313 mn np mq 138 1 314 mn pq pq 154 1 315 mn m n 130, 146 2 316 mn n m 130, 138 2 317 mn p q 138, 154 2 318 mn q p 146, 154 2
 321 mq mn mq 132 1 322 mq mq no conclusion 147-148, 162, 164, 178-180 7 323 mq np mq 140 1 324 mq pq not-n 155-156, 170, 172, 186-188 7 325 mq m no conclusion 132, 147-148, 162, 164, 178-180 8 326 mq n mq 132, 140 2 327 mq p not-n 140, 155-156, 170, 172, 186-188 8 328 mq q no conclusion 147-148, 155-156, 162, 164, 170, 172, 178-180, 186-188 14 331 np mn np 194 1 332 np mq np 210 1 333 np np no conclusion 74, 78, 134, 142, 198, 202, 206 7 334 np pq not-m 90, 94, 150, 158, 214, 218, 222 7 335 np m np 194, 210 2 336 np n no conclusion 74, 78, 134, 142, 194, 198, 202, 206 8 337 np p no conclusion 74, 78, 90, 94, 134, 142, 150, 158, 198, 202, 206, 214, 218, 222 14 338 np q not-m 90, 94, 150, 158, 210, 214, 218, 222 8 341 pq mn pq 196 1 342 pq mq not-m 211-212, 226, 228, 242-244 7 343 pq np not-n 76, 80, 136, 144, 200, 204, 208 7 344 pq pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 49 345 pq m not-m 196, 211-212, 226, 228, 242-244 8 346 pq n not-n 76, 80, 136, 144, 196, 200, 204, 208 8 347 pq p no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 144, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 348 pq q no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 159-160, 166, 168, 174, 176, 182-184, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 56 351 m mn m 130, 132 2 352 m mq no conclusion 146-148, 162, 164, 178-180 8 353 m np mq 138, 140 2 354 m pq not-n 154-156, 170, 172, 186-188 8 355 m m no conclusion 130, 132, 146-148, 162, 164, 178-180 10 356 m n m 130, 132, 138, 140 4 357 m p not-n 138, 140, 154-156, 170, 172, 186-188 10 358 m q no conclusion 146-148, 154-156, 162, 164, 170, 172, 178-180, 186-188 16 361 n mn n 130, 194 2 362 n mq np 146, 210 2 363 n np no conclusion 74, 78, 134, 138, 142, 198, 202, 206 8 364 n pq not-m 90, 94, 150, 154, 158, 214, 218, 222 8
 365 n m n 130, 146, 194, 210 4 366 n n no conclusion 74, 78, 130, 134, 138, 142, 194, 198, 202, 206 10 367 n p no conclusion 74, 78, 90, 94, 134, 138, 142, 150, 154, 158, 198, 202, 206, 214, 218, 222 16 368 n q not-m 90, 94, 146, 150, 154, 158, 210, 214, 218, 222 10 371 p mn p 194, 196 2 372 p mq not-m 210-212, 226, 228, 242-244 8 373 p np no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 198, 200, 202, 204, 206, 208 14 374 p pq no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 375 p m not-m 194, 196, 210-212, 226, 228, 242-244 10 376 p n no conclusion 74, 76, 78, 80, 134, 136, 142, 144, 194, 196, 198, 200, 202, 204, 206, 208 16 377 p p no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 142, 144, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 198, 200, 202, 204, 206, 208, 214-216, 218-220, 222-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 70 378 p q no conclusion 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 150-152, 158-160, 166, 168, 174, 176, 182-184, 190-192, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 64 381 q mn q 132, 196 2 382 q mq no conclusion 147-148, 162, 164, 178-180, 211-212, 226, 228, 242-244 14 383 q np not-n 76, 80, 136, 140, 144, 200, 204, 208 8 384 q pq no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 56 385 q m no conclusion 132, 147-148, 162, 164, 178-180, 196, 211-212, 226, 228, 242-244 16 386 q n not-n 76, 80, 132, 136, 140, 144, 196, 200, 204, 208 10 387 q p no conclusion 76, 80, 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 136, 140, 144, 151-152, 155-156, 159-160, 166, 168, 170, 172, 174, 176, 182-184, 186-188, 190-192, 200, 204, 208, 215-216, 219-220, 223-224, 230, 232, 234, 236, 238, 240, 246-248, 250-252, 254-256 64 388 q q no conclusion 91-92, 95-96, 106, 108, 110, 112, 122-124, 126-128, 147-148, 151-152, 155-156, 159-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 211-212, 215-216, 219-220, 223-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 70

If we compare the results of microanalysis listed in the above table with those obtained by macroanalysis (those listed in chapter 6, and again in Tables 7.3, 7.4 and 7.5, and those listed in Tables 9.4 and 9.5), we discover that they are in most cases apparently inconsistent! However, before making any hasty judgments, it is well to become aware that many apparent similarities between the cases treated are in fact superficial, so that differences in result should come as no surprise.

We could at this stage create a table listing all positive moods in the three figures in one column, the collected positive and negative conclusions by macroanalysis in a second column, and the above conclusions obtained by microanalysis in a third column. Then, in a fourth column, we would want to explain, case by case, why any eventual divergences occurred. However, it is still too early for such a systematic comparison between our approaches, for reasons that will become clear in the following comments.

In the above table, we are dealing with only three items, P, Q and R. The weak determinations considered are always absolute (involving 108 alternative moduses in the PQR matrix). It follows that even when one or both premises are weak, the syllogism is always in subfigure ‘a’[6].

We cannot, therefore, compare the conclusions obtained here to those previously found, when a subsidiary item (S) was specified and the minor item (P) was occasionally found as a complement in the major premise (as in subfigure ‘d’ and others). Here, when a weak determination (absolute) is affirmed or denied in premise(s) and/or in conclusion, the effective moduses might concern the subsidiary item or its negation, or the minor, middle or major item or its negation, or again some other item entirely!

We must thus tread very carefully before making comparisons. It is ultimately only by developing four-item microanalysis, and thereby four-item syllogism, that mechanical comparisons with macroanalysis can safely be made. We will consequently abstain from such consistency checking for now, while acknowledging its ultimate importance. Let us rather at this stage continue to develop three-item syllogistic theory. Some of these developments will clarify the issue raised here, as we shall see.

We shall now deal with three-item syllogism with vague premises; that is, strong causation (s = m or n), absolute weak causation (wabs = pabs or qabs), or absolute causation (cabs = s or wabs = m or n or pabs or qabs). What we shall find is that no conclusion arises from any combination of such premises (with each other – we shall not bother to deal with combinations of vague premises with more precise premises, regarding them as practically unlikely to arise). This is an interesting result, though negative.

The following table merges the moduses of precise positive premises (given in Table 14.3, above), to obtain those of vague positive premises with forms s, wabs or cabs. Note well that each of these forms is fully convertible, i.e. is the same for two given items whatever their positions (QR and RQ have the same moduses, PQ and QP have the same moduses).

Table 14.5. Enumeration of three-item alternative moduses for vague positive premises, for any figure of syllogism.

 Determ. Major QR Major RQ Minor PQ Minor QP s = m or n 10, 12, 14, 25-30, 42, 44, 57-60, 74, 78, 89-90, 93-94, 130, 132, 134, 138, 140, 142, 145-150, 153-158, 162, 164, 170, 172, 177-180, 185-188, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222 10, 12, 14, 25-30, 42, 44, 57-60, 74, 78, 89-90, 93-94, 130, 132, 134, 138, 140, 142, 145-150, 153-158, 162, 164, 170, 172, 177-180, 185-188, 194, 198, 202, 206, 209-210, 213-214, 217-218, 221-222 66-68, 70-72, 74-76, 78-80, 82-84, 98-100, 114-116, 130-132, 134-136, 138-140, 142-144, 146-148, 162-164, 178-180, 194-196, 198-200, 202-204, 206-208, 210-212, 226-228, 242-244 66-68, 70-72, 74-76, 78-80, 82-84, 98-100, 114-116, 130-132, 134-136, 138-140, 142-144, 146-148, 162-164, 178-180, 194-196, 198-200, 202-204, 206-208, 210-212, 226-228, 242-244 wabs = pabs or qabs 12, 14, 16, 27-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 132, 134, 136, 140, 142, 144, 147-152, 155-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256 12, 14, 16, 27-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 132, 134, 136, 140, 142, 144, 147-152, 155-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256 cabs = m or n or pabs or qabs 10, 12, 14, 16, 25-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 130, 132, 134, 136, 138, 140, 142, 144-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256 10, 12, 14, 16, 25-32, 42, 44, 46, 48, 57-64, 74, 76, 78, 80, 89-96, 106, 108, 110, 112, 121-128, 130, 132, 134, 136, 138, 140, 142, 144-160, 162, 164, 166, 168, 170, 172, 174, 176-192, 194, 196, 198, 200, 202, 204, 206, 208-224, 226, 228, 230, 232, 234, 236, 238, 240-256 66-68, 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 130-132, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 194-196, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256 66-68, 70-72, 74-76, 78-80, 82-84, 86-88, 90-92, 94-96, 98-100, 102-104, 106-108, 110-112, 114-116, 118-120, 122-124, 126-128, 130-132, 134-136, 138-140, 142-144, 146-148, 150-152, 154-156, 158-160, 162-164, 166-168, 170-172, 174-176, 178-180, 182-184, 186-188, 190-192, 194-196, 198-200, 202-204, 206-208, 210-212, 214-216, 218-220, 222-224, 226-228, 230-232, 234-236, 238-240, 242-244, 246-248, 250-252, 254-256

As the table below shows, no positive or negative conclusion is obtainable from two vague positive premises (any combination of s, wabs, cabs). This means one has to go to a more precise level – of generics or joints – to obtain a conclusion in positive causative syllogism.

Note that the three figures yield the same moduses in each mood. This is because, as indicated above, the premises involved have the same moduses whatever the orientation of the items concerned (i.e. they are all fully convertible).

Table 14.6. Moduses of conclusions for selected vague positive premises.

 Major Minor Conclusion First Figure QR PQ PR Second Figure RQ PQ PR Third Figure QR QP PR For all three figures Common moduses No. s s no conclusion 74, 78, 130, 132, 134, 138, 140, 142, 146-148, 162, 164, 178-180, 194, 198, 202, 206, 210 21 s wabs no conclusion 74, 78, 90, 94, 134, 138, 140, 142, 146-148, 150, 154-156, 158, 162, 164, 170, 172, 178-180, 186-188, 198, 202, 206, 210, 214, 218, 222 33 wabs s no conclusion 74, 76, 78, 80, 132, 134, 136, 140, 142, 144, 147-148, 162, 164, 178-180, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 226, 228, 242-244 33 wabs wabs no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 140, 142, 144, 147-148, 150-152, 155-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 93 s cabs no conclusion 74, 78, 90, 94, 130, 132, 134, 138, 140, 142, 146-148, 150, 154-156, 158, 162, 164, 170, 172, 178-180, 186-188, 194, 198, 202, 206, 210, 214, 218, 222 36 cabs s no conclusion 74, 76, 78, 80, 130, 132, 134, 136, 138, 140, 142, 144, 146-148, 162, 164, 178-180, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 226, 228, 242-244 36 wabs cabs no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 132, 134, 136, 140, 142, 144, 147-148, 150-152, 155-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 96 cabs wabs no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 134, 136, 138, 140, 142, 144, 146-148, 150-152, 154-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 96 cabs cabs no conclusion 74, 76, 78, 80, 90-92, 94-96, 106, 108, 110, 112, 122-124, 126-128, 130, 132, 134, 136, 138, 140, 142, 144, 146-148, 150-152, 154-156, 158-160, 162, 164, 166, 168, 170, 172, 174, 176, 178-180, 182-184, 186-188, 190-192, 194, 196, 198, 200, 202, 204, 206, 208, 210-212, 214-216, 218-220, 222-224, 226, 228, 230, 232, 234, 236, 238, 240, 242-244, 246-248, 250-252, 254-256 100

This table is interesting in that it shows that no causative conclusion can be drawn from vague causative premises in any of the three figures. In particular, it answers one of our first questions, teaching us that, generally speaking, if P causes Q and Q causes R, it does not follow that P causes R.

[6] See chapter 5 for the list of subfigures.

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